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Is there a term describing a specialised solver which is used as a subroutine or a different, larger solver?

For example, a gradient descent solver which, at each step, uses a line search to optimise what step size to take. I'm after a term to describe that line search algorithm in the context of it being a subroutine of some other, larger algorithm.

The best I could come up with so far is either a 'subsolver' (but I think that means something else already?) or 'hyposolver' (as a contrast to a solver used for hyperparameter optimisation). Both of these are, however, just terms I came up with rather than part of a more established nomenclature.

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Lower level optimization problems being solved within a top or higher level algorithm are called subproblems.

So the algorithm or routine to solve subproblems could be called a "subproblem solver". Googling "subproblem solver" shows that this term is not that uncommon. If there is a specific type of subproblem being solved, that can be incorporated, such as "QP subproblem solver" of an SQP algorithm, LP subproblem solver of a MILP solver, local nonlinear subproblem solver of a branch and bound global optimization solver.

In the case of line search, that would usually be called a line search algorithm. line search routine, or similar variation.

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